Confused on what to do ?! Ex girlfriend drama

so me & my boyfriend were "talking" for about 3 months before his girlfriend at the time contacted me out of nowhere to tell me that they've been together for 7 months & he wasn't single . at the time , I just shrugged it off because he was the one trying really hard to pursue me while I had the mindset that all guys were fvck boys & he knew that . about two months later , he texts me paragraphs telling me that he was really sorry about how things went down & that he's been trying to figure out how to approach me for an entire month . he told me that him & his ex broke up shortly after I found out about them & that he's willing to do whatever it takes to build my trust back . after a couple of paragraphs of him telling me how much I meant to him & how sorry & confused he was at the time when everything went down , I ended up giving him a second chance to prove himself to me . he drove an hour to my college & hung out with me that entire day the next day . in a span of a month , he has given me the info to two of his credit cards , let me follow his location to see where he was at all times & bought me gifts without me even asking . so at the end of the month he proved to me that he deserved my trust so we made it official . then this is when his ex started coming back into the picture . so far me & my boyfriend have been officially dating for 2 months & his ex has posted different photos of them as her header on twitter , put his name in her bio , has got into my boyfriend's twitter account to change his header and bio , blocked me from her account & his account on twitter , blocked me from her snapchat & his snapchat , has called me from a blocked number at 3am to tell me to stop talking to her boyfriend or else she was going to fight me , has hit me up on snapchat (before she blocked me) to ask if I was still talking to her man . in the midst of all that , I've told my boyfriend to change his passwords but she also has access to his email address & seems to change his new passwords that way . i've told him to change his email password & he told me he did but she STILL has access to his accounts . after a couple weeks of this happening I started to accuse my boyfriend cause this was getting really ridiculous & Ive never heard of a girl being so adamant about a guy being her man when he doesn't want anything to do with her . he's proceeded to tell me that he doesn't want her whatsoever & even gave me her number to talk to her myself since I didn't believe him . I texted her & asked her nicely if she would back off & asked her if she & my boyfriend were back together . & she told me that they did break up but she just misses him & would back off but I felt like that was too easy which it was because she's still continuing to post old photos of her & my boyfriend . idk what to do at this point because my gut feeling isn't telling me that my boyfriend is playing me again mainly because he's given me her number & his credit card info & I feel like a guy wouldn't do that for a girl he was just trying to play . my boyfriend tells me all the time that he cares about me so much & proves nothing less . it's just his ex that is making me insecure because he's gotten back with her before so he might do it again , you know ? what should I do ?